Sparse Bayesian Learning for a Bilinear Calibration Model and Mismatched CRB

Abstract

Variational Bayesian (VB) estimation allows for approximate Bayesian inference. It determines the closest approximation in factored form of the posterior distribution by minimizing the Kullback-Leibler distance to the posterior distribution even if this last one is difficult to determine. In spite of this well motivated derivation, the performance of VB techniques is not very clear, especially compared to more classical performance bounds. In this paper we explore recently introduced mismatched Cramer-Rao bounds (mCRB) for Bayesian estimation in the context of VB estimation. We focus on the case of bilinear signal models. One particular application of these models arises in the context of internal relative reciprocity calibration of Massive antenna arrays, in which the received signals are linear in terms of an intra array channel and the relative calibration factors. We have recently shown that a VB approach allows for particularly improved estimation performance that goes beyond the classical CRB, which is now confirmed by the mCRB.